There's more ... but not just now._________________"Method goes far to prevent trouble in business: for it makes the task easy, hinders confusion, saves abundance of time, and instructs those that have business depending, both what to do and what to hope."
William Penn 1644-1718

It is rather simple - a dictionary would be able to assist you so could search on google or even the ITIL glossary

Customers buy the service
Users use the service

But customers don't typically "order" the services right?

and often but not always, customers use the services.

Plus the users often have their own customers who derive value from the services that neither the user or these customers buy...right?

it really depends on the service that is being consumed, whether by a customer, a user or a user's customer.
_______________________

The ITIL definitions are easy to understand. But in terms of an example:

Say the service is an insurance company's claims system.
[list=]The Business Manager from the Insurance company buys the "claims service/system". In ITIL terms he is the customer.
The insurance claims officer who processes claims uses the system. Thus is the user.
The public who have their claims processed are the insurance company's customers but they are neither customers or users of the service. Unless they make online/phone claims into a claims service, in which case they are users of the system.[/list]

Basically it is clear as mud, so all thsat matters is that whatever terms you use in your company, everyone understands everyone...

For a thousand quid a day, I'll even explain it upside down._________________"Method goes far to prevent trouble in business: for it makes the task easy, hinders confusion, saves abundance of time, and instructs those that have business depending, both what to do and what to hope."
William Penn 1644-1718